One of the explanations given for the unusual power-law growth of the human species given by von Foerster is the higher connectivities among humans in terms of information flow, enabling technological developments through invention and diffusion, and also enabling humans to form lesser or grand collaborative coalitions in a game against nature to improve (or destroy) the carrying capacity of the environment. Von Foerster treats this connectivity as a relative constant in the time period of this graph, but comments that this may be a further variable to examine in connection with such models at earlier time periods.
Part of the reason for cycling around a von Foerster regression line in human population growth may be temporary Malthusian constraints of reaching environmental limits. Another is sociopolitical violence, which seems to kick in as these constraints are reached, among other factors.
Part of the objective of the macromodeling papers in this symposium
should be to replicate the von Foerster graph with current data that also
reachs further back in time to include historical and archaeological time
periods, and to investigate whether there are deviations from this model,
either at transition points (phase transitions) or in cyclical deviations,
amplification or reduction of cyclical deviations, and lengthening or
shortening of cycles. Future research will need to test whether this type of
model replicates regionally, and test the effects of changes in connectivity.
The degree of multiconnectivity in trade and/or warfare networks, for example,
may prove to be an important variable.
Click the image to enlarge and print.
Thurs Feb 24th - General Program
Pop Den & Growth 1961
Von Foerster at Wenner Gren 1964
biography of Von Foerster 1964
Umpleby on Foerster 2001
Foerster Bibliography 2001
Nathan Keyfitz. 1975. How Do We Know the Facts of Demography?, Population and Development Review 1(2): 267-288. Population Growth and Earth's Human Carrying Capacity
Joel E. Cohen 1995. Science 269(5222): 341-346.
Kapitza on Quadratic Growth
http://eclectic.ss.uci.edu/SF/Russian Conference 2004
From DRWHITE@uci.edu Fri Dec 17 11:31:10 2004 Date: Fri, 17 Dec 2004 09:28:25 -0800 (PST) From: Doug
To: Andrey Korotayev Cc: Artemy Malkov , Daria Khaltourina , Douglas R White Subject: Re: http://eclectic.ss.uci.edu/SF/S.Fe04.htm the pdfs can each be downloaded from the web. They include letters and reponses by Foester et a, later commentary. Foester covers almost all of what we have talked about (including technology, dynamical instabilities and transition points, ect.). Totally consistent with Artemy's framework. Here is my current thinking. All but two of Foerster's data points are between 1750 - 1960. As with Artemy's framework, Foerster indicates that where N --> infinity there is an instability point. The data now compiled goes back to -10,000 and further. For the period prior to 500BCE we can ask and computed whether there is the same type of log-log curve for population and population density. If we plot our data on his p.1294 curve that seems a good way to begin. The data point for 500BCE is very close to his line. But as we go back to 8000BCE our points go down very steeply to fit his curve. One hypothesis is that our data are inaccurate, underestimates as we go further back in time. Another is that Foester's equation sets are correct, but there is a transition point where the constants in the equations change. Do we also have the data on areas for our early data fit to his curve, i.e., calculating population density? Say we concluded that Foester's equation sets (3)-(9) hold, but with different constants (10)-(13). Then what accounts for the discontinuity? One possibility is that there was an instability near 500BCE with these constants. But is that date anywhere near an instability for N --> infinity? Other are that connectivity changed. Or technology changed. But once we go this route, since these are also gradual changes, we need to account for criticalities in one or more of the variables we introduce. And these should relate to the "grand coalition" idea of Foester perhaps, or game against nature. Because the curves before and after 500BCE are so great, I think these are the questions we need to address first, along with the question of how accurate are the estimates for the early period. If we are successful for this transtion, then we can apply the same approach and questions to the period from 500BCE to approximately 1500 CE plus or minus 200 years, where there is another more subtle transition. I would not like to hear more talk about changes in world system, expressed quantitatively. I would like to see all such arguments phrased in terms of measureable variables. Doug White, professor, UC Irvine http://eclectic.ss.uci.edu ------------- From email@example.com Fri Dec 17 08:38:43 2004 Date: Mon, 13 Dec 2004 06:23:36 +0300 From: fabr To: Douglas R. White Cc: KOROTAYEV@YAHOO.COM, Andrey Korotayev , Peter Turchin , Don Saari Subject: Re: some loose ends Let me get into your discussion. It seems to me that my physical point of view will assist you in clarification of the macromodel implementation. Dynamics of every physical body is influences by a huge number of factors. Modern physics abundantly evidences it. Even if consider a falling ball, we inevitably face such forces as gravitation, friction, electromagnetic forces, forces caused by pressure, by radiation, by anisotropy of medium and so on. All these forces do have effect on motion of considered body. It is a physical fact. Consequently in order to describe this motion we should construct an equation involving all these factors. Only in this case we may "guarantee" the right description. Moreover, even these equation is not right! Because we have not included the factors and forces which ACTUALLY EXIST but are NOT YET INVENTED! It is evident that such a puristic approach and a rush for precision lead to agnosticism and nothing else. Fortunately, from the physical point of view, all the processes have their characteristic time scales and their application conditions. Even if there is a great number of significant factors we can sometimes neglect all of them except the most evident one. There are two main cases of simplification: 1. When force, caused by selected factor is much more than all other forces. 2. When selected factor has a characteristic time scale which is adequate to the scale of considered process, while all other factors have much different time scales (less or more - does not matter) The first case seems to be clear. As for second, it is substantiated by Tikhonov theorem (1952). It states that if there is a system of three differential equations, and if the first variable is changing very quickly, the second changes very slowly, and the third is changing with an acceptable characteristic time scale, then we can discard the first and the second equations and pay attention only to the third one. In this case first equation must be solved as a algebraic equation (not as a differential), and the second variable must be handled as a parameter. Let's consider some extremely complicated process. For example, photosynthesis. Characteristic time scales are the following (in seconds): 1. light absorption: ~ 0.000000000000001 2. reaction of charge separation: ~ 0.000000000001 3. electron transport: ~ 0.0000000001 4. carbon fixation: ~ 1 - 10 5. transport of nutrients: ~ 100 - 1000 6. plant growth ~ 10000 - 100000 Such a spread in scales allows constructing rather simple and valid models for every scale without involving all these processes into consideration. Each time scale has its own laws and equations that are limited by the corresponding conditions. If the system exceeds the limits of respective scale, its behaviour will change, and equations will also change. It is not a defect of description - it is just a transition from one regime to another. For example, solid bodies can be described perfectly by solid models having respective equations and laws of motion (e.g. mechanics of rigid body) , but increasing the temperature will cause melting process, and the same body will convert into liquid, which must me described by absolutely different laws (e.g. hydrodynamics), finally the same body converts into gas and obeys respective laws (e.g. Boyle's law etc.) It may look like a mystification. The same body may obey different laws and equations when temperature changes SLIGHTLY! But it is a fact. Moreover, from the microscopic point of view - all these laws originate from micro interaction of molecules, which remain the same for solid body, liquids and gases. But from the point of view of macro processes, macro-behavior is different and equations are different. So there is noting abnormal that the dynamics of complex system is described has phase transition and sudden changes of regimes. For every change in physics there are always limitations that change the law of change in the neighborhood of limit. Examples of such limitations are absolute zero of temperature and velocity of light. If temperature is big enough or, respectively, velocity is small, then classical laws are working perfectly, but if temperature is close to absolute zero or velocity is close to velocity of light - then behavior may change incredibly. Such effects as superconductivity or space-time distortion may be observed. As for demographic growth, there are a number of limitations, each of them having their characteristic scales and applicability conditions. Analyzing the system we can define some of these limitations. Growth is limited by: 1. RESOURCE limitations: 1.1. starvation - if there is no food (or other significant for vital functions resources) there can be no growth, but collapse time scale ~ 0.1 - 1 year conditions: RESOURCE SHORTAGE This is a strong limitation and it works inevitably. 1.2. technological - technology may support a limited number of workers time scale of ~ 10-100 YEARS conditions: TECHNOLOGY IS "LOWER" THAN POPULATION this is a relatively rapid process, which causes demographic cycles. 2. BIOLOGICAL 2.1. birth rate - a woman cannot produce more than 1 child per year (while a man can do :) time scale ~ 1 year condition: BIRTH RATE (CHILDREN PER WOMAN) is VERY HIGH This is a very strong limitation with a short small time scale, so it will be the only rule of growth if for any of possible reasons respective condition (birth rate is very high) will be observed. 2.2. pubescence - a woman cannot produce children until she is mature time scale ~ 15-20 years conditions: EARLY CHILD-BEARING This condition is less strong than 2.1. but in fact condition 2.1. is rarely observed. For real demographic processes limitation 2.2. is more essential than 2.1. because for premodern societies women start giving birth being 15-20 years old. 3. SOCIAL 3.1. infant mortality - mortality is obviously preventing population growth time scale ~ 1-5 years condition: LOW HEALTH PROTECTION Short time scale - strong and actual limitation for premodern societies. 3.2. mobility - in preagrarian societies woman cannot have many children, cause it reduces mobility. time scale: ~3 years condition: WANDERING TRIBES 3.3. education - education increases the "cost" of individual, but requires years of education, making the procreation undesirable. High human-cost allows an educated person to stand on his own legs until his old age, without help of his children. These limitations reduce birth rate. time scale: ~25-40 years condition: HIGH EDUCATION All these limitations are objective. But each of them is ACTUAL (that is it must be included into equations) ONLY IF RESPECTIVE CONDITIONS ARE OBSERVED. If for any considered historical period several limitations are actual (under their conditions) then, neglecting the others, equation for this period must involve their implementation. According to Tikhonov theorem the most strong of them are ones having shortest time scale. HOWEVER, factors with longer time scale may "start working" under less severe requirements, making short-time-scale factors not actual, but POTENTETIAL Lets observe and analyze the following epochs: I. pre-agrarian societies II. agrarian societies III. post-agrarian societies using such a notation: - atypical - means that the properties of the epoch make the conditions practically impossible. - actual - means that such conditions are observed, so this limitation is actual and must be involved into implementation - potential - means that such conditions are not observes but if some other limitations will be removed, this limitation may become actual I. pre-agrarian societies limitations: 1.1. - ACTUAL * 1.2. - ACTUAL ** 2.1. - potential 2.2. - ACTUAL 3.1. - ACTUAL 3.2. - ACTUAL 3.3. - atypical II. agrarian societies 1.1. - ACTUAL 1.2. - ACTUAL 2.1. - potential 2.2. - ACTUAL 3.1. - ACTUAL 3.2. - atypical 3.3. - potential II. post-agrarian societies 1.1. - atypical 1.2. - potential/actual *** 2.1. - potential 2.2. - potential 3.1. - atypical 3.2. - atypical 3.3. - ACTUAL ------ * systematic (not an occasional short term) starvation is caused by misbalance of technology and population, so 1.1. may be included into 1.2. ** according to Tikhonov theorem we may neglect the oscillations of population (demographic cycles), because their time scales are at least 10 times less than the scale of historical period that is taken into account. *** technology produces much more than it is necessary for the sustenance, but the living standards also require more resources In our macromodel we involve only agrarian and post-agrarian societies (for leak of data for preagrarian societies) According to Tikhonov theorem to describe the DYNAMICS of the system we should take actual factor, which has the LONGEST time-scale (it will represent dynamics, while shorter scale factors will be involved as coefficients - solutions of algebraic equations), So epoch [II] is characterized by 1.2, and [III] - by 3.3 ([III] also involves 1.2, but for [III] resource limitation 1.2 is much less essential, cause it concerns life standards, and not vitally important needs) Thus, demographic transition is a process of transition from II:[1.2] --> to III:[3.3] Limitation 3.3 at [III] makes biological limitations unessential but potential. (possibly, in future, limitation 3.3 could be reduces, for example, reducing time of education thanks to higher educational technologies, so it will make [2.2] actual again; possibly cloning will make [2.1] and [2.2] obsolete - so there will become apparent new limitations) In conclusion, I want to note, that hyperbolic growth is a feature which corresponds to II:[1.2], there is no contradiction between hyperbolic growth itself and [2.1] or [2.2]. Hyperbolic agrarian growth does never reach the birth-rate, which is close to conditions of [2.1]. If it was so, hyperbola will obviously convert into exponent, when birth-rate will come close to [2.1] (just as physical velocity may never exceed the velocity of light) - and it would be not a weakness of model, just a common sense. It would be [1.2] -> [2.1, 2.2] But actual demographic transition [1.2] -> [2.1] is more drastic than this [1.2] -> [2.1, 2.2]! [3.3] is reducing birth-rate much more actively, and it may seem strange though SOCIETY WAS MUCH CLOSER TO [2.1] and [2.2] WHAN IT WAS GROWING SLOWER - during the epoch of [II]! (it is not nonsense because slower growth was the reason of [2.1] and [3.1]) As for the after-doomsday dynamics, - I said - if there is no resource of spatial limitation, (as well as [3.1]) - then the [2.1] and [2.2] will become actual. If they will also be removed (cloning, etc.) then there will appear new limitations. But if we consider the solution of C/(t0 - t) just formally - the after-doomsday dynamics has no sense. But it normal, such as temperature below absolute zero, or velocity above velocity of light have no sense. As for statistical problem of "one series" - it actually exists! however, the stability of the system (perfect hyperbola for population and pretty-good GDP hyperbola) gives us hopes for macro-law definition. The more serious problem having one series is to distinguish which is primary - GDP or population and which is proportion. I am absolutely agree, that the most important direction of future research is to find and analyze "several independent series" (dynamics for pre-Columbian Afroeurasia, America, Australia etc.) even through it will be an arduous task. Sincerely, A.Malkov DRW> Right - but I disagree in the following way. Consider removing the DRW> constraints the way that Newton does for the falling apple to get the DRW> gravity results. That is, would the hyperbolic, now in discrete form with DRW> ca. 20 year generations on average between births still make sense IF DRW> THERE WERE NO RESOURCE OR SPATIAL CONSTRAINTS? That is, if you DRW> extrapolated to AFTER DOOMSDAY? Would world population INTRINSICALLY begin DRW> to fall semi-hyperbolically and in reverse? Absolutely not! This is what DRW> you have to do when you look for "mechanisms" underlying equations. DRW> Say you fit the equation for an orbit around the sun. Now take away the DRW> sun. Do you suppose the movement will follow the orbit just because you DRW> have an equation? I.e., don't privilege the equation over the physics and DRW> the experimental method of the sciences generally. DRW> As Saari and Turchin would say, you have to lay out a large potential set DRW> of possible dynamic equations delta Y = f(A,B,C) where you think you know DRW> the things -- MEASURABLE THINGS -- that affect changes in Y, but there are DRW> a variety of ways that these may interrelate with an unknown number of DRW> stable and unstable equilibria. The problem is NOT JUST TO ASSUME ONE DRW> EQUATION IS RIGHT BECAUSE IT FITS SOME DATA FOR ONE INTERVAL IN ONE TIME DRW> SERIES (your fallacious macromodeling approach) but to investigate using DRW> measurable variables multiple cases where you can observe the dynamics of DRW> interactions among these observables. >> Dear Doug, DRW> The correct interpretation of von Foerster's finding would have been just DRW> that the world demographic growth reached such a point that its basic DRW> pattern was bound to get radically changed well before 2026. And this DRW> prediction would have started to get confirmed within a very few years DRW> after 1960. We have rather frequently growth patterns described accurately DRW> by certain equations, which when extrapolated produce absurd results, and DRW> this just says that the respective growth pattern will get changed well DRW> before the date of predicted absurd result. Take for example the simplest DRW> demographic model dN/dt = aN. Does it make sense? Yes, it does, as, DRW> ceterum paribus, 10 million mothers would give birth to approximately 10 DRW> times more babies than 1 million mothers. Do we observe things like 2% DRW> annual growth rates for some periods of time? However, what will we have DRW> if we extrapolate this pattern observed in a certain country (of say 10 DRW> mln people) in future? Just in 350 years we will have 10 bln people, in DRW> 700 years 10 trillion, and in 1050 we will have 10000 trillion. Is this DRW> result absurd? Perhaps, somehow. But in fact, it just shows that the DRW> respective growth pattern cannot last for long, as, e.g., "ceterum DRW> paribus" implies the same level of resource provision and the country DRW> resource growth 1 billion times is simply impossible (let alone lots of DRW> other things). This simply means that the respective growth pattern will DRW> get transformed in a fairly near future. The same goes for hyperbolic DRW> growth patterns (both in physics and social life), which are bound to get DRW> transformed into non-hyperbolic dynamics at certain points.